Exp Brain Res (1999) 125:139–152

© Springer-Verlag 1999

R E S E A R C H A RT I C L E

R E S E A R C H A RT I C L E Julie Messier · John F. Kalaska

Comparison of variability of initial kinematics and endpoints of reaching movements

Received: 23 March 1998 / Accepted: 2 September 1998

Abstract The accuracy of reaching movements to memorized visual target locations is presumed to be determined largely by central planning processes before movement onset. If so, then the initial kinematics of a pointing movement should predict its endpoint. Our study examined this hypothesis by testing the correlation between peak acceleration, peak velocity, and movement amplitude and the correspondence between the respective spatial positions of these kinematic landmarks. Subjects made planar horizontal reaching movements to targets located at five different distances and along five radially arrayed directions without visual feedback during the movements.The spatial dispersion of the positions of peak acceleration, peak velocity, and endpoint all tended to form ellipses oriented along the movement trajectory. However, whereas the peaks of acceleration and velocity scaled strongly with movement amplitude for all of the movements made at the five target distances in any one direction, the correlations with movement amplitude were more modest for trajectories aimed at each target separately. Furthermore, the spatial variability in direction and extent of the distribution of positions of peak acceleration and peak velocity did not scale differently with target distance, whereas they did for endpoint distributions. Therefore, certain features of the final kinematics are evident in the early kinematics of the movements as predicted by the hypothesis that they reflect planning processes. However, endpoint distributions were not completely predetermined by the Initial kinematics. In contrast, multivariate analysis suggests that adjustments to movement duration help compensate for the variability of the initial kinematics to achieve desired movement amplitude. These compensatory adjustments do not conJ. Messier · J.F. Kalaska (✉) Centre de Recherche en Sciences Neurologiques, Département de Physiologie, Faculté de médecine, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montreal, Canada, QC H3C 3J7 e-mail: [email protected] Tel.: +1-514-343-6349, Fax: +1-514-343-6113

tradict the general conclusion that the systematic patterns in the spatial variability observed in this study reflect planning processes. On the contrary, and consistent with that conclusion, our results provide further evidence that direction and extent of reaching movements are planned and determined in parallel over time. Key words Reaching movements · Direction · Amplitude · Initial kinematics · Spatial variability · Human

Introduction An important approach to investigating how the motor system plans reaching movements has been to identify invariant patterns in their spatiotemporal form (Soechting and Flanders 1989; Flanders et al. 1992). These motor invariances are assumed to reflect the parameters in which reaching movements are represented at different stages of the planning process. Several stereotypical patterns characterize the extrinsic kinematics (spatiotemporal pattern of displacement of the hand) of unobstructed reaching movements to targets. First, the path of the movement is essentially straight (Morasso 1981; Abend et al. 1982; Atkeson and Hollerbach 1985; Georgopoulos and Massey 1988; Gordon et al. 1994b). Second, velocity profiles are single-peaked and bell-shaped (Morasso 1981). Third, peak acceleration and peak velocity scale systematically with movement amplitude (Atkeson and Hollerbach 1985; Gordon et al. 1994a). Since these kinematic parameters of the early part of the reach trajectory correlate with the direction and distance of target location, movement extent and movement direction would appear to be largely specified before movement onset and to influence the initiation of movement. It is also widely accepted that the accuracy of reaching movements to memorized visual target locations is determined largely by planning processes before movement onset (Soechting and Flanders 1989; Flanders et al. 1992). Based on the measurements of the accuracy in

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pointing to memorized target locations, a number of studies suggested that direction and extent of reaching movements are relevant control parameters (Bock and Arnold 1992; Gordon et al. 1994a, 1994b). In these studies, patterns of errors could not be explained by poor memory, poor perception of target locations, or by peripheral biomechanical factors arising during movement execution (Soechting and Flanders 1989; Gordon et al. 1994b; Berkinblit et al. 1995; Messier and Kalaska 1997a). Instead they were attributed to central planning processes, especially putative early transformations from spatial to limb-centered motor coordinates (Soechting and Flanders 1989; Flanders et al. 1992). If the dispersion of endpoints of reaching movements are mostly related to movement planning and are consequently predetermined before the initiation of movement, then the initial kinematics of pointing movements should predict the endpoint distribution. This study examined this hypothesis by testing the correspondence between endpoint variability patterns and the variability of the (x,y) coordinates of positions of peak acceleration and velocity. We found that certain features of the spatial distribution of endpoints are evident in the early kinematics of the movements. However, the modest correspondence between these distributions on a trial-by-trial basis indicates that the endpoints of reaching movements are not completely predetermined by the initial kinematics in a simple ballistic manner. In contrast, evidence suggests that compensatory adjustments are made to correct for initial variability in the directionality of movements and in the scaling of peak acceleration and peak velocity with target distance. A preliminary report of these results has been presented (Messier and Kalaska 1997b).

Materials and methods Subjects Subjects were seven neurologically normal adults (five women and two men) with ages ranging from 20 to 33 years. They participated voluntarily in this study. All subjects were right-handed and used their right arm to execute the pointing movements in this experiment. They signed a consent form, and the experimental protocol was approved by the University Human Research Ethics Committee. Participants were naive about the purpose of the experiment. Recording of kinematics of arm movements and task The task, task apparatus, and methods are described in detail in a previous paper (task 2 of Messier and Kalaska 1997a). Briefly, subjects made planar horizontal reaching movements from a common starting position to 25 targets located at five different distances (4, 8, 16, 24, 32 cm) along five movement directions (0°, 45°, 90°, 135°, and 180°, with 0° to the right). The subjects’ arm was in a parasagittal plane and was unsupported against gravity during the movements. Subjects wore a therapeutic brace to immobilize the wrist and to maintain the index finger in a fixed pointing posture. The spatial trajectory of the index finger between start and endpoint was recorded at a sampling frequency of 100 Hz using an Optotrak 3020 motion analysis system. The start position and tar-

Fig. 1 Schematic representation of the experimental setup. The subjects sat in a chair in front of a horizontal plane (table) positioned slightly above the waist. The start position displayed on the computer monitor screen corresponded to a position midway between the right shoulder and the body midline on the horizontal plane. The spatial coordinates of a light-emitting diode fixed on the index fingertip of subjects was recorded using an Optotrak 3020 motion analysis system. The cloth barrier preventing view of the arm is not shown get location were displayed on a computer monitor screen positioned at eye level and 1 m in front of the subjects (Fig. 1). There was an arbitrary scaling factor of 1:2.4 between the movement amplitudes displayed on the screen and the movement amplitudes made by the subjects. An opaque cloth suspended horizontally between the monitor and the subject prevented any visual feedback from the arm during the movements. Before data collection, each subject had a brief practice session to familiarize themselves with the targets located on the monitor and the corresponding reaching movements. During data collection, the trajectory of the index finger and the position of the target were displayed on the monitor during the intertrial interval after the completion of each reaching movement. Data analysis Many of the details of the data analysis are described in a previous paper (Messier and Kalaska 1997a). Multiple approaches were used to analyze the spatial variability along the reach trajectories. First, the recorded spatial coordinates (x,y) of the movement handpath of each response were filtered using a fourth-order, zero phase-shift Butterworth filter (Winter 1990) with a cutoff frequency of 14 Hz (FiltFilt function, Matlab; The Math Works). The xand y-axes of the Cartesian coordinate system were aligned to the directional axes, with the positive x-axis at 0°and the positive yaxis at 90°.Tangential velocities and acceleration were computed using standard differentiation techniques, and peak velocity and acceleration were determined. Movement onset was defined as the first time the tangential velocity exceeded 1 cm/s and remained above that value until peak velocity was attained. Similarly, the end of the movement was defined as the first time tangential velocity decreased below 1 cm/s. The linearity of movement trajectories were computed for each movement using the index developed by Atkeson and Hollerbach (1985). Briefly, the linearity index is the ratio between the largest deviation of the actual movement trajectory perpendicular to a straight line between the start

141 Fig. 2A–D Methods used to determine spatial positions and spatial distribution of positions of peak acceleration, peak velocity, and endpoint of movements. Acceleration (A) and velocity (B) profiles for one trial by one subject, and, the corresponding positions of peak acceleration (1), peak velocity (2), and movement end (3) on the handpath (C). D shows the spatial distribution of the (x,y) positions of peak acceleration (1), peak velocity (2), and endpoints (3) for 20 movements aimed at a single target. The size, shape, and orientation of the ellipses were determined using principal component analysis (Sokal and Rohlf 1981). The axes in C and D indicate the (x,y) coordinates in cm, relative to the start position at (0.0)

and the endpoint of each movement and the length of that straight line. The spatial position (x,y) at which peak acceleration and peak velocity occurred were determined for the 20 trials directed to each target and compared with the spatial distribution of the (x,y) positions of endpoints (Fig. 2). First, variable errors of direction (off-axis errors) and extent (on-axis errors) were computed for each of these distributions along the reach trajectories (see Messier and Kalaska 1997a for details). Second, the spatial dispersion of these three distributions were characterized using principal component analysis (Sokal and Rohlf 1981). This method allows the determination (within 95% confidence limits) of the size, the shape, and the orientation of the spatial dispersion across trials of positions of peak acceleration, peak velocity, and endpoint along the movement path. Third, a trial-by-trial analysis was used to test the degree of correlation between each of these successive kinematic landmarks of the reaching movements. Correlation coefficients were computed between the values of peak acceleration, peak velocity and movement amplitude and also between variable errors of direction and extent for the spatial distribution of positions of peak acceleration, peak velocity, and endpoint. The latter analysis tests the tendency of the spatial position of the peak acceleration, peak velocity, and endpoint for a given trial to occupy the same relative position within the distribution of each landmark for the 20 trials aimed at a target. These correlation coefficients were calculated for the trajectories across all five targets along a single direction, as well as for trajectories aimed at each of the 25 targets separately for each subject. Fourth, a statistical model was tested (Fig. 3) to assess whether compensatory adjustments come into play during the movements (Gordon and Ghez 1987). The proportion of variance in peak acceleration and velocity explained by target distance is estimated by the squared correlation coefficient r21.2, while the extent to which movement amplitude is determined by peak acceleration and velocity is estimated by the squared correlation coefficient r2Y.1.The hatched arrow in Fig. 3 represents the corrective effects of the target distance, which is the independent effect of the target distance on the movement amplitude (Gordon and Ghez 1987).

Fig. 3 Statistical model used to assess the compensatory effects of target distance for initial variability in the scaling of peak acceleration and peak velocity. The simple squared correlation coefficients r21.2 and r2Y.1 represent the proportion in the variance accounted for by the target distance and the peaks of acceleration and velocity in determining movement amplitude. They are both used as independent variables in the calculation of R2Y1.2, which is the multiple correlation coefficient between X1, X2, and Y (from Gordon and Ghez 1987)

This independent effect of target distance can be assessed in two steps. First, the coefficient of multiple determination R2Y1.2 (Sokal and Rohlf 1981) represents the proportion of the variation in movement amplitude explained by the combined effect of target distance (X2) and the peak acceleration or velocity (X1) on the movement amplitude. Second, the difference between R2Y1.2 and r2Y.1 extracts the contribution of peak acceleration or velocity (X1) to the prediction of movement amplitude. As a result, this difference corresponds to the independent effect of target distance on the actual movement amplitude. Whether the target’s influence is compensatory, i.e., whether it increases significantly the proportion of the variance in movement amplitude explained was tested

142 by using a multiple regression analysis (Sokal and Rohlf 1981). This approach tested the effect of adding target distance (X2) to the regression equation predicting movement amplitude (Y) from peak acceleration or peak velocity (X1), i.e., from Y=a+bX1 to Y=a+b1X1+b2X2. The significance test for this analysis was an Fstatistic and was performed for each direction and for each subject using the following formula (Sokal and Rohlf 1981): FS = ( RY21.2 − rY2.1 )/(k2 − k1 ) (1 − RY21.2 )(n − k2 − 1) where k1 is number of variables in the initial regression equation (k1=1, X1) and k2 is the total number of variables considered in the analysis, i.e., including the added variable(s) (k2=2, X1 and X2). The n-value is the number of movements in the sample.The critical value of FS is given by Fα[k2–k1, n–k2–1], where α is level of statistical significance. Fig. 4 Hand trajectories for 20 movements aimed at targets in five different directions and five different distances by one subject. The axes indicate displacement in cm

Fig. 5 Mean velocity profiles of 20 movements aimed at each of 25 targets located in five different distances and five different directions, for the movements shown in Fig. 4

Results In this study we examined the hypothesis that the endpoint distributions of reaching movements to memorized visual target locations are completely predetermined by central planning processes occurring before the initiation of movement. If this hypothesis is true in the strictest sense, the initial kinematics of pointing movements should predict the endpoint distributions. The characteristics of variability of initial and final kinematics of reaching movements were compared using two main approaches. First, principal component analysis was used to compare the form, the size, and the orientation of the

143 Fig. 6 Mean acceleration profiles across 20 movements aimed to each of 25 targets located in five different distances and five different directions, made by the same subject as in Fig. 4

endpoint distributions with spatial distributions of the (x,y) coordinates of position of peak acceleration and velocity. Second, a trial-by-trial correlation analysis was used to evaluate the degree of predictability between those events along the movement paths. Finally, a statistical procedure was used to examine whether the variance in movement amplitude not explained by the initial kinematics can be in part accounted for by corrective adjustments to other movement parameters. General observations The kinematics of the reach trajectories were characterized by the same ensemble of properties described in other studies (Fig. 2). Hand trajectories were approximately straight, with a mean linearity index of 0.025 across all subjects. Figure 4 shows hand paths to the 25 different targets (five directions for each distance) for one typical subject. Velocity profiles were single-peaked and bell-shaped (Figs. 2, 5) and both peak velocity and acceleration increased with increasing movement amplitude in all directions tested (Figs. 5, 6). This relationship was tested on a trial-trial basis for all movements to the five targets along each movement direction, for each subject (Fig. 7). The resulting correlations were very high between peak acceleration and peak velocity (mean r=0.934), and between peak velocity and movement extent (mean r=0.926). The correlation between peak acceleration and movement extent was somewhat lower (mean r=0.794). Across a wide range of distances, therefore, the initial kinematics of the movements scaled systematically with movement extent. The time at which the peak values of acceleration and veloci-

Fig. 7 Mean correlation coefficients between each kinematic landmark along the reach trajectories for movements aimed at all five target distances along each of the five directions separately (n=5 directions × 7 subjects). The first bar represents the mean correlation coefficient between the peaks of acceleration and velocity (A/V). The second bar represents the mean correlation coefficient between the peaks of velocity and endpoint distances (V/E), while the third bar represents the mean correlation coefficient between the peaks of acceleration and endpoint distances (A/E). The error bars indicate standard deviation of the mean across seven subjects. The ratio above each bar represents the proportion of significant (P